Sift flour, sugar, and salt in a large bowl; add 2 tablespoons of the butter. Blend in a mixer until the dough resembles coarse cornmeal or blend with two hands / pastry blender. Add the rest of the butter; mix everything until the biggest pieces look like large sized peas.

Slowly add in water, stir, then slowly add in more until the dough just holds together. Toss with hands, letting it fall through your fingers, until it’s ropy with some dry patches. If dry patches predominate, add another tablespoon water. Keep tossing until you can roll the dough into a ball. Flatten into a 4-inch-round disk; refrigerate. After at least 30 minutes, remove; let soften so it’s malleable but still cold. Smooth cracks at edges. On a lightly floured surface, roll into a 14-inch circle about 1/8 inch thick. If you are using a squared tart pan, you want to roll the dough out into a rectangle. Dust excess flour from both sides with a dry pastry brush.

Place the dough in a lightly greased 9-inch round or squared tart pan, or simply on a parchment-lined baking sheet if you wish to go free-form, or galette-style with it. Preheat oven to 400ºF.

Overlap the apples on the dough in a ring 2 inches from edge if using a round tart pan. If using a rectangular tart pan, overlap the apples in even columns. If going galette-style, or up to the sides if using the tart pan. Continue inward until you reach the center. Fold any dough hanging over pan back onto itself; crimp edges at 1-inch intervals.

Brush melted butter over apples and onto dough edge. Sprinkle 2 tablespoons sugar over dough edge and the other 3 tablespoons over apples. You definitely will not be able to put all 5 tablespoons of sugar on this tart. It’s just too much! But if you can, more power to you!

Bake in center of oven until apples are soft, with browned edges, and crust has caramelized to a dark golden brown (about 45 minutes), making sure to rotate tart every 15 minutes.

Make glaze: Put reserved peels and cores in a large saucepan, along with sugar. Pour in just enough water to cover; simmer for 25 minutes. Strain syrup through cheesecloth.